op
Einleitung

\subsection{Themen}

\begin{itemize}
  \item Heidelberg bla
  \item Galaxy Foo bla
  \item Stauchen / Strecken bla
  \item Problem: Geschwindigkeit bla
  \item Benchmarks:
  \begin{itemize}
    \item 10000 Sterne - 1 Stern
    \item ...
  \end{itemize}
\end{itemize}

\subsection{Motivation}

\paragraph{ \( \Phi \) }

\begin{equation}
  \Phi(r) = - \frac{4\pi G \rho_0 R_s^3}{r} \ln ( 1+ \frac{r}{R_s} )
\end{equation}

with the limits

\begin{equation}
  \lim_{r\to \infty} \Phi=0
\end{equation}

and

\begin{equation}
  \lim_{r\to 0} \Phi=-4\pi G\rho_0 R_s^2
\end{equation}

\paragraph{ \( \rho \) }

\begin{equation}
  \rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot
  e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)}
\end{equation}

\paragraph{\( \rho_{new} \rightarrow (deriviation) \) }

\begin{equation}
  \rho(r) \cdot 1-\frac{1}{(2 \cdot sigma^{2} )} \cdot
  ( Mxx \cdot x^{2} + 2 \cdot Mxy \cdot xy + Myy \cdot y^{2} ))
\end{equation}

% def rho_new(x, y, z):
%     a = (1 - ((1) / (2 * (sigma ** 2))) * ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) )
%     return rho(x, y, z) * a
%
% # phi function
% def phi(x):
%     if x == 0:
%         return -4 * pi * f_0 * G * R_s**2
%
%     a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x
%     b = np.log(1. + (x / R_s) )
%     c = a * b
%     return c

Motivations blah